# Loading sequentially R codes
source("load-data-ts.R")
source("tf_apl.R")
source("tf_fb_sci.R")
source("tf_sg.R")
Loading data from Facebook Symptoms datasets and other public datasets for analysis:
This data contains device change in mobility using Jan 13th, 2020 as reference to track changes.
fb_df_tarrant %>%
melt(id.vars = c("date"), measure.vars = c("cli", "cmnt_cli")) %>%
group_by(variable) %>%
group_map(~plot_ly(.,x=~date, y=~value,color = ~variable, mode = "lines"), keep=TRUE) %>%
subplot(nrows = 1, shareX = TRUE, shareY = FALSE) %>%
layout(title="Facebook CLI vs Community CLI")
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NA
head(fb_df_tarrant)
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sg_df_tarrant %>%
plot_ly(x=~date) %>%
add_trace(y=~fulltime, mode="lines", name="Fulltime") %>%
add_trace(y=~parttime, mode="lines", name="Parttime")
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head(sg_df_tarrant)
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apple_mob_tarrant %>%
plot_ly(x=~date) %>%
add_trace(y=~driving, mode="lines", name="driving") %>%
add_trace(y=~walking, mode="lines", name="walking") %>%
add_trace(y=~transit, mode="lines", name="transit") %>%
layout(title="Apple mobility data")
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From apple data, we create a composite indicator by combining the effect of driving and transit variables into a single variable which the transit ratio to transit + driving. \(transit/(transit+driving)\). This variable is calculated based on the assumption that the higher the transit, the higher the risk of infection and the higher the driving, the lower the risk of infection, hence driving is at the denominator of the formula and transit as well is there to normalize the value between 0 and 1.
plot_ly(data = df_final, x=~date) %>%
add_trace(y=~comp_indice, mode="lines") %>%
layout(title="Apple Mobility Composite indicator", yaxis=list(title="Mobility index"))
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df_final
NA
##############################################################
# NEW PHASE #
############## Vector Error correction Model #################
require(bvartools)
require(urca)
require(vars)
require(dynlm)
require(forecast)
k <- nrow(df_final)-14
##############################################################
#### Making the dataset stationary by first differencing ####
df_final_ts <- ts(df_final[1:k,-1])
df_final_ts_sta <- diff(df_final_ts,1)
##############################################################
############## Creating the test timeseries ##################
df_test <- na.omit(df_final[(k+1):nrow(df_final),])
df_test_ts <- ts(df_test[,-c(1:2)])
### Stationarizing the test dataset
df_test_ts_sta <- diff(df_test_ts,1)
df_1 <- df_final[1:k,-1]
names(df_1) <- c("Positivity", "CLI", "Community_CLI", "Fulltime", "Partime", "Apple_comp_index")
plot(ts(df_1), main="Figure 1: Time series plot non-stationary")
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NA
This is the representation of the time series after applying the first difference with the first lag value
df_2 <- df_final[1:k,-1]
names(df_2) <- c("Positivity", "CLI", "Community_CLI", "Fulltime", "Partime", "Apple_comp_index")
df_2 <- na.omit(diff(ts(df_2), 1))
plot(df_2, main="Figure 1: Time series plot non-stationary")
source("functions.R")
##############################################################
################## VAR MODEL BUILDING ########################
#Lag selection
var_lag <- VARselect(df_final_ts, lag.max = 8, type = "both", season = 7)
# Extracting the lag seleciton by AIC
max_lag = as.numeric(var_lag$selection[1])
## Option 1: VAR Model
VAR_pos <- VAR(df_final_ts, lag.max = max_lag, type = "both", season = 7)
summary(VAR_pos$varresult$pos_ma)
Call:
lm(formula = y ~ -1 + ., data = datamat)
Residuals:
Min 1Q Median 3Q Max
-0.42436 -0.05971 0.01085 0.08425 0.27286
Coefficients:
Estimate Std. Error t value Pr(>|t|)
pos_ma.l1 8.070e-01 1.998e-01 4.040 0.00122 **
cli.l1 -1.344e+00 7.440e-01 -1.807 0.09235 .
cmnt_cli.l1 -1.036e-01 2.014e-01 -0.514 0.61519
fulltime.l1 -3.338e+02 3.578e+02 -0.933 0.36665
parttime.l1 5.891e+01 2.913e+02 0.202 0.84267
comp_indice.l1 7.240e+00 1.090e+01 0.664 0.51746
pos_ma.l2 -1.970e-01 2.707e-01 -0.728 0.47882
cli.l2 1.447e+00 1.069e+00 1.354 0.19704
cmnt_cli.l2 -1.664e-01 2.121e-01 -0.785 0.44567
fulltime.l2 6.934e+02 3.602e+02 1.925 0.07481 .
parttime.l2 -4.368e+02 2.932e+02 -1.490 0.15848
comp_indice.l2 -1.618e+01 7.338e+00 -2.204 0.04473 *
pos_ma.l3 2.846e-01 2.261e-01 1.259 0.22864
cli.l3 -5.064e-01 1.363e+00 -0.372 0.71571
cmnt_cli.l3 8.607e-02 2.750e-01 0.313 0.75889
fulltime.l3 9.978e+01 3.372e+02 0.296 0.77165
parttime.l3 -1.659e+02 2.700e+02 -0.615 0.54874
comp_indice.l3 4.801e-01 1.076e+01 0.045 0.96504
pos_ma.l4 1.901e-01 2.538e-01 0.749 0.46621
cli.l4 2.206e+00 1.466e+00 1.505 0.15462
cmnt_cli.l4 5.248e-01 2.410e-01 2.177 0.04707 *
fulltime.l4 -1.840e+02 4.026e+02 -0.457 0.65463
parttime.l4 3.534e+02 3.106e+02 1.138 0.27429
comp_indice.l4 9.183e+00 9.580e+00 0.959 0.35402
pos_ma.l5 -6.050e-01 2.438e-01 -2.482 0.02639 *
cli.l5 -2.958e-01 1.375e+00 -0.215 0.83274
cmnt_cli.l5 -3.461e-01 2.412e-01 -1.435 0.17316
fulltime.l5 -2.157e+02 3.661e+02 -0.589 0.56504
parttime.l5 -8.510e+01 3.041e+02 -0.280 0.78366
comp_indice.l5 4.262e+00 9.446e+00 0.451 0.65876
pos_ma.l6 1.400e-01 2.241e-01 0.625 0.54232
cli.l6 -8.240e-01 1.284e+00 -0.642 0.53138
cmnt_cli.l6 -1.576e-02 2.102e-01 -0.075 0.94128
fulltime.l6 -1.035e+02 4.156e+02 -0.249 0.80689
parttime.l6 2.932e+02 3.356e+02 0.874 0.39703
comp_indice.l6 1.880e+01 1.037e+01 1.813 0.09126 .
pos_ma.l7 -2.797e-01 2.090e-01 -1.338 0.20220
cli.l7 6.313e-01 1.294e+00 0.488 0.63330
cmnt_cli.l7 3.847e-01 1.945e-01 1.978 0.06795 .
fulltime.l7 1.993e+02 4.068e+02 0.490 0.63184
parttime.l7 -3.576e+02 3.081e+02 -1.161 0.26525
comp_indice.l7 -1.566e-01 8.060e+00 -0.019 0.98477
pos_ma.l8 2.256e-01 1.876e-01 1.203 0.24907
cli.l8 -2.810e-01 8.901e-01 -0.316 0.75692
cmnt_cli.l8 -3.878e-01 1.495e-01 -2.595 0.02120 *
fulltime.l8 -7.788e+01 3.522e+02 -0.221 0.82821
parttime.l8 1.488e+02 2.626e+02 0.567 0.57995
comp_indice.l8 2.031e+01 9.156e+00 2.218 0.04360 *
const -2.266e+00 2.026e+01 -0.112 0.91253
trend -2.384e-03 2.416e-02 -0.099 0.92281
sd1 9.671e-01 3.097e-01 3.122 0.00749 **
sd2 8.229e-01 3.740e-01 2.200 0.04507 *
sd3 9.718e-01 3.634e-01 2.675 0.01814 *
sd4 7.229e-01 4.056e-01 1.782 0.09640 .
sd5 7.702e-01 4.186e-01 1.840 0.08710 .
sd6 6.906e-01 4.253e-01 1.624 0.12674
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2939 on 14 degrees of freedom
Multiple R-squared: 0.9972, Adjusted R-squared: 0.986
F-statistic: 89.66 on 55 and 14 DF, p-value: 6.546e-12
coeftest(VAR_pos$varresult$pos_ma)
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
pos_ma.l1 8.0700e-01 1.9976e-01 4.0399 0.001217 **
cli.l1 -1.3442e+00 7.4404e-01 -1.8067 0.092350 .
cmnt_cli.l1 -1.0355e-01 2.0142e-01 -0.5141 0.615188
fulltime.l1 -3.3379e+02 3.5777e+02 -0.9330 0.366651
parttime.l1 5.8907e+01 2.9134e+02 0.2022 0.842674
comp_indice.l1 7.2397e+00 1.0903e+01 0.6640 0.517464
pos_ma.l2 -1.9699e-01 2.7073e-01 -0.7276 0.478821
cli.l2 1.4474e+00 1.0686e+00 1.3545 0.197039
cmnt_cli.l2 -1.6643e-01 2.1208e-01 -0.7848 0.445674
fulltime.l2 6.9339e+02 3.6023e+02 1.9248 0.074814 .
parttime.l2 -4.3683e+02 2.9323e+02 -1.4897 0.158483
comp_indice.l2 -1.6176e+01 7.3382e+00 -2.2044 0.044729 *
pos_ma.l3 2.8464e-01 2.2610e-01 1.2589 0.228637
cli.l3 -5.0642e-01 1.3626e+00 -0.3717 0.715711
cmnt_cli.l3 8.6075e-02 2.7500e-01 0.3130 0.758894
fulltime.l3 9.9779e+01 3.3720e+02 0.2959 0.771646
parttime.l3 -1.6590e+02 2.6998e+02 -0.6145 0.548740
comp_indice.l3 4.8013e-01 1.0760e+01 0.0446 0.965040
pos_ma.l4 1.9013e-01 2.5382e-01 0.7491 0.466211
cli.l4 2.2063e+00 1.4663e+00 1.5047 0.154621
cmnt_cli.l4 5.2480e-01 2.4105e-01 2.1772 0.047068 *
fulltime.l4 -1.8402e+02 4.0262e+02 -0.4571 0.654633
parttime.l4 3.5338e+02 3.1058e+02 1.1378 0.274293
comp_indice.l4 9.1831e+00 9.5796e+00 0.9586 0.354020
pos_ma.l5 -6.0500e-01 2.4380e-01 -2.4815 0.026392 *
cli.l5 -2.9583e-01 1.3749e+00 -0.2152 0.832736
cmnt_cli.l5 -3.4615e-01 2.4116e-01 -1.4353 0.173162
fulltime.l5 -2.1573e+02 3.6607e+02 -0.5893 0.565038
parttime.l5 -8.5103e+01 3.0407e+02 -0.2799 0.783662
comp_indice.l5 4.2620e+00 9.4460e+00 0.4512 0.658757
pos_ma.l6 1.3996e-01 2.2410e-01 0.6245 0.542317
cli.l6 -8.2399e-01 1.2839e+00 -0.6418 0.531382
cmnt_cli.l6 -1.5763e-02 2.1019e-01 -0.0750 0.941281
fulltime.l6 -1.0354e+02 4.1565e+02 -0.2491 0.806895
parttime.l6 2.9318e+02 3.3557e+02 0.8737 0.397032
comp_indice.l6 1.8799e+01 1.0367e+01 1.8134 0.091260 .
pos_ma.l7 -2.7969e-01 2.0903e-01 -1.3381 0.202201
cli.l7 6.3128e-01 1.2944e+00 0.4877 0.633298
cmnt_cli.l7 3.8474e-01 1.9451e-01 1.9780 0.067950 .
fulltime.l7 1.9927e+02 4.0681e+02 0.4898 0.631837
parttime.l7 -3.5758e+02 3.0812e+02 -1.1605 0.265247
comp_indice.l7 -1.5664e-01 8.0604e+00 -0.0194 0.984769
pos_ma.l8 2.2561e-01 1.8759e-01 1.2026 0.249067
cli.l8 -2.8097e-01 8.9011e-01 -0.3157 0.756922
cmnt_cli.l8 -3.8782e-01 1.4947e-01 -2.5946 0.021197 *
fulltime.l8 -7.7881e+01 3.5224e+02 -0.2211 0.828206
parttime.l8 1.4880e+02 2.6262e+02 0.5666 0.579954
comp_indice.l8 2.0309e+01 9.1563e+00 2.2181 0.043597 *
const -2.2664e+00 2.0263e+01 -0.1119 0.912530
trend -2.3835e-03 2.4160e-02 -0.0987 0.922812
sd1 9.6714e-01 3.0974e-01 3.1224 0.007491 **
sd2 8.2287e-01 3.7397e-01 2.2004 0.045068 *
sd3 9.7180e-01 3.6335e-01 2.6745 0.018138 *
sd4 7.2290e-01 4.0561e-01 1.7822 0.096402 .
sd5 7.7015e-01 4.1861e-01 1.8398 0.087099 .
sd6 6.9058e-01 4.2532e-01 1.6237 0.126736
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The model shows 5 point of cointegration by the values of r based on the Johanssen Cointegration testing procedure
##############################################################
################## VECM MODEL BUILDING #######################
k_order <- VAR_pos$p
vecm_model1 <- ca.jo(df_final_ts, ecdet = "none", type = "trace", K=k_order, spec = "transitory")
vecm_model2 <- ca.jo(df_final_ts, ecdet = "none", type = "trace", K=k_order, spec = "transitory", season = 7)
summary(vecm_model2)
######################
# Johansen-Procedure #
######################
Test type: trace statistic , with linear trend
Eigenvalues (lambda):
[1] 0.74897060 0.69483276 0.57991029 0.56611234 0.26541745 0.09155884
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 5 | 6.72 6.50 8.18 11.65
r <= 4 | 28.31 15.66 17.95 23.52
r <= 3 | 86.76 28.71 31.52 37.22
r <= 2 | 147.47 45.23 48.28 55.43
r <= 1 | 230.55 66.49 70.60 78.87
r = 0 | 327.31 85.18 90.39 104.20
Eigenvectors, normalised to first column:
(These are the cointegration relations)
pos_ma.l1 cli.l1 cmnt_cli.l1 fulltime.l1 parttime.l1 comp_indice.l1
pos_ma.l1 1.0000000 1.000000 1.000000 1.0000000 1.000000e+00 1.000000e+00
cli.l1 -3.0630550 -3.760839 -3.636171 -1.8949559 3.210515e+01 1.022709e+00
cmnt_cli.l1 0.1418586 4.807900 -2.802619 -0.5026748 -9.783487e-02 -9.549848e-02
fulltime.l1 -223.0901159 5311.200058 -774.263425 -1008.0009570 -3.202675e+03 -8.500281e+03
parttime.l1 732.8951483 263.268810 -3949.644214 846.7288028 3.161644e+03 7.249906e+03
comp_indice.l1 50.4456482 -234.182382 -1949.173112 -117.5251941 -2.581604e+02 6.647874e+02
Weights W:
(This is the loading matrix)
pos_ma.l1 cli.l1 cmnt_cli.l1 fulltime.l1 parttime.l1 comp_indice.l1
pos_ma.d -3.591411e-01 -1.076634e-02 -2.791261e-02 -0.0219036829 -8.589304e-03 2.233327e-03
cli.d -1.647736e-03 7.846280e-03 5.615503e-03 0.0120897714 -6.588928e-03 -3.071758e-03
cmnt_cli.d 1.429612e-01 4.563878e-02 -1.551966e-02 -0.4713334183 1.185956e-02 -1.646780e-02
fulltime.d 4.510599e-05 -1.578786e-04 6.818415e-06 -0.0001274476 -6.405771e-05 -7.634917e-06
parttime.d -9.125754e-05 -1.866555e-04 2.066501e-05 -0.0005979152 -7.710192e-05 1.842888e-06
comp_indice.d -1.575304e-03 -5.549697e-05 9.002646e-04 -0.0050749134 5.019504e-04 -2.126127e-04
plt_R
[[1]]
[[2]]
[[3]]
[[4]]
[[5]]
NA
mape_R
[1] 7.953662
##### Test with full data
#Lag selection
var_lag1 <- VARselect(df_full_ts, lag.max = 8, type = "both", season = 7)
# Extracting the lag seleciton by AIC
max_lag1 = as.numeric(var_lag1$selection[1])
## Option 1: VAR Model
VAR_pos1 <- VAR(df_full_ts, lag.max = max_lag, type = "both", season = 7)
summary(VAR_pos1$varresult$pos_ma)
Call:
lm(formula = y ~ -1 + ., data = datamat)
Residuals:
Min 1Q Median 3Q Max
-0.53270 -0.12753 -0.00723 0.14189 0.65938
Coefficients:
Estimate Std. Error t value Pr(>|t|)
pos_ma.l1 7.302e-01 1.596e-01 4.575 8.85e-05 ***
cli.l1 -4.392e-01 7.609e-01 -0.577 0.5684
cmnt_cli.l1 2.193e-02 1.758e-01 0.125 0.9016
fulltime.l1 -5.622e+02 3.142e+02 -1.790 0.0843 .
parttime.l1 3.056e+02 2.376e+02 1.286 0.2089
comp_indice.l1 -2.385e+00 8.258e+00 -0.289 0.7749
pos_ma.l2 -3.397e-02 2.061e-01 -0.165 0.8703
cli.l2 7.305e-01 8.534e-01 0.856 0.3992
cmnt_cli.l2 -1.605e-03 2.070e-01 -0.008 0.9939
fulltime.l2 7.674e+02 3.789e+02 2.025 0.0525 .
parttime.l2 -4.404e+02 2.971e+02 -1.483 0.1494
comp_indice.l2 -1.221e+01 7.162e+00 -1.705 0.0992 .
pos_ma.l3 1.706e-01 2.042e-01 0.836 0.4105
cli.l3 -6.269e-01 9.565e-01 -0.655 0.5176
cmnt_cli.l3 -1.378e-01 2.264e-01 -0.609 0.5477
fulltime.l3 -4.678e+02 3.652e+02 -1.281 0.2107
parttime.l3 3.039e+02 2.795e+02 1.087 0.2862
comp_indice.l3 -5.032e+00 7.478e+00 -0.673 0.5065
pos_ma.l4 1.095e-01 2.066e-01 0.530 0.6003
cli.l4 1.403e+00 1.159e+00 1.211 0.2362
cmnt_cli.l4 2.062e-01 2.224e-01 0.927 0.3616
fulltime.l4 3.841e+02 3.899e+02 0.985 0.3330
parttime.l4 -1.299e+02 2.949e+02 -0.440 0.6630
comp_indice.l4 -1.252e+00 7.633e+00 -0.164 0.8709
pos_ma.l5 -8.603e-02 2.097e-01 -0.410 0.6848
cli.l5 -4.620e-01 1.225e+00 -0.377 0.7089
cmnt_cli.l5 -1.920e-01 1.916e-01 -1.002 0.3248
fulltime.l5 -4.923e+01 3.979e+02 -0.124 0.9024
parttime.l5 -2.029e+02 3.105e+02 -0.654 0.5187
comp_indice.l5 1.181e+01 8.411e+00 1.405 0.1712
pos_ma.l6 4.217e-02 1.966e-01 0.215 0.8317
cli.l6 6.116e-01 1.181e+00 0.518 0.6087
cmnt_cli.l6 -1.329e-01 1.820e-01 -0.730 0.4713
fulltime.l6 -1.179e+02 3.895e+02 -0.303 0.7643
parttime.l6 2.029e+02 3.167e+02 0.641 0.5269
comp_indice.l6 2.353e+00 8.839e+00 0.266 0.7920
pos_ma.l7 -2.747e-01 1.994e-01 -1.378 0.1792
cli.l7 -1.430e+00 1.145e+00 -1.249 0.2219
cmnt_cli.l7 4.568e-01 1.882e-01 2.428 0.0219 *
fulltime.l7 1.745e+02 3.780e+02 0.462 0.6479
parttime.l7 -2.230e+02 2.963e+02 -0.753 0.4579
comp_indice.l7 1.209e+01 7.335e+00 1.648 0.1105
pos_ma.l8 2.112e-01 1.623e-01 1.301 0.2037
cli.l8 8.005e-01 7.989e-01 1.002 0.3249
cmnt_cli.l8 -2.207e-01 1.411e-01 -1.564 0.1292
fulltime.l8 -1.518e+02 3.005e+02 -0.505 0.6174
parttime.l8 1.389e+02 2.214e+02 0.627 0.5355
comp_indice.l8 4.300e+00 7.476e+00 0.575 0.5698
const 1.770e-01 5.909e+00 0.030 0.9763
trend 1.897e-02 1.420e-02 1.336 0.1923
sd1 3.692e-01 2.848e-01 1.296 0.2054
sd2 7.708e-01 3.619e-01 2.130 0.0421 *
sd3 6.949e-01 3.951e-01 1.759 0.0896 .
sd4 4.818e-01 3.671e-01 1.312 0.2000
sd5 5.321e-01 3.997e-01 1.331 0.1938
sd6 -1.408e-01 3.752e-01 -0.375 0.7102
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3788 on 28 degrees of freedom
Multiple R-squared: 0.9912, Adjusted R-squared: 0.9741
F-statistic: 57.67 on 55 and 28 DF, p-value: < 2.2e-16
k_order1 <- VAR_pos1$p
vecm_model11 <- ca.jo(df_full_ts, ecdet = "none", type = "trace", K=k_order, spec = "transitory")
vecm_model21 <- ca.jo(df_full_ts, ecdet = "none", type = "trace", K=k_order, spec = "transitory", season = 7)
summary(vecm_model21)
######################
# Johansen-Procedure #
######################
Test type: trace statistic , with linear trend
Eigenvalues (lambda):
[1] 0.634688487 0.543896242 0.318314083 0.257413375 0.124878165 0.003740139
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 5 | 0.31 6.50 8.18 11.65
r <= 4 | 11.52 15.66 17.95 23.52
r <= 3 | 36.52 28.71 31.52 37.22
r <= 2 | 68.71 45.23 48.28 55.43
r <= 1 | 134.65 66.49 70.60 78.87
r = 0 | 219.24 85.18 90.39 104.20
Eigenvectors, normalised to first column:
(These are the cointegration relations)
pos_ma.l1 cli.l1 cmnt_cli.l1 fulltime.l1 parttime.l1 comp_indice.l1
pos_ma.l1 1.000000 1.000000 1.0000000 1.00000 1.000000 1.0000000
cli.l1 -6.077475 -8.090654 -0.4007323 -44.10591 -4.373226 -4.7241972
cmnt_cli.l1 -6.835700 -2.594450 -0.2700501 -1.43946 0.479617 0.2376699
fulltime.l1 -9334.324692 -3190.270551 -900.5471740 3483.59746 -3325.101247 420.2072931
parttime.l1 3308.323566 365.226034 953.4601694 -3949.64766 3133.694358 255.7459101
comp_indice.l1 689.757393 289.505559 -82.3971774 -383.70258 -23.139995 -81.7596070
Weights W:
(This is the loading matrix)
pos_ma.l1 cli.l1 cmnt_cli.l1 fulltime.l1 parttime.l1 comp_indice.l1
pos_ma.d 3.766836e-02 -8.446051e-02 -0.0797529129 -1.894378e-03 -1.840294e-02 8.570906e-03
cli.d -7.255163e-03 -3.541575e-03 0.0127383094 8.235237e-03 2.100576e-03 8.804290e-05
cmnt_cli.d -2.858606e-02 1.627182e-02 0.0809155956 -5.732026e-03 -4.453219e-02 -1.339407e-02
fulltime.d 3.466038e-05 9.102563e-05 -0.0001571358 3.258298e-05 -3.612136e-05 1.795908e-05
parttime.d 1.015895e-05 9.599685e-05 -0.0004022396 3.284365e-05 -4.678241e-05 3.270886e-05
comp_indice.d -5.511619e-04 -3.345934e-04 0.0055034738 -4.418049e-05 -2.522533e-04 5.019480e-04
save(VAR_pos_Rs, "VAR_pos_Rs.rda")
Error in save(VAR_pos_Rs, "VAR_pos_Rs.rda") :
object ‘VAR_pos_Rs.rda’ not found